In this seminar, the participants will present a variety of classical results in the (widely understood) area of discrete mathematics (graph theory, additive number theory, discrete geometry, etc.) that have short elegant proofs. Among other sources, the topics will be selected from the books "The Art of Mathematics: Coffee Time in Memphis" by Bollobás and "Proofs from THE BOOK" by Aigner and Ziegler.
The seminar has no prerequisites, but it will be conducted in English.
B. Bollobás, The Art of Mathematics: Coffee Time in Memphis, Cambridge University Press, 2006
M. Aigner, G. Ziegler, Proofs from THE BOOK, 5th edition, Springer, 2014
Introduction; presentation of topics
Two problems about tiling rectangles
Sperner's theorem and the Littlewood–Offord problem
Bootstrap percolation in the integer lattice
Three lemmas in additive combinatorics
The Kakeya problem over finite fields
The Erdős–Ko–Rado theorem and the chromatic number of the Kneser graph
Lattice paths and determinants
Three theorems in discrete convex geometry
Shannon capacity of C5